Measures Integrals And Martingales

Author : René L. Schilling
Publisher : Cambridge University Press
ISBN 13 : 1316620247
Total Pages : 497 pages
Book Rating : 4.43/5 ( download)

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Download or read book Measures, Integrals and Martingales written by René L. Schilling and published by Cambridge University Press. This book was released on 2017-04-03 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.

Author : René L. Schilling
Publisher : Cambridge University Press
ISBN 13 : 9780521850155
Total Pages : 404 pages
Book Rating : 4.50/5 ( download)

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Download or read book Measures, Integrals and Martingales written by René L. Schilling and published by Cambridge University Press. This book was released on 2005-11-10 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.

Author : René L. Schilling
Publisher : Cambridge University Press
ISBN 13 : 1009020390
Total Pages : 431 pages
Book Rating : 4.98/5 ( download)

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Download or read book Counterexamples in Measure and Integration written by René L. Schilling and published by Cambridge University Press. This book was released on 2021-06-17 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Often it is more instructive to know 'what can go wrong' and to understand 'why a result fails' than to plod through yet another piece of theory. In this text, the authors gather more than 300 counterexamples - some of them both surprising and amusing - showing the limitations, hidden traps and pitfalls of measure and integration. Many examples are put into context, explaining relevant parts of the theory, and pointing out further reading. The text starts with a self-contained, non-technical overview on the fundamentals of measure and integration. A companion to the successful undergraduate textbook Measures, Integrals and Martingales, it is accessible to advanced undergraduate students, requiring only modest prerequisites. More specialized concepts are summarized at the beginning of each chapter, allowing for self-study as well as supplementary reading for any course covering measures and integrals. For researchers, it provides ample examples and warnings as to the limitations of general measure theory. This book forms a sister volume to René Schilling's other book Measures, Integrals and Martingales (www.cambridge.org/9781316620243).

Author : Marek Capinski
Publisher : Springer Science & Business Media
ISBN 13 : 1447136314
Total Pages : 229 pages
Book Rating : 4.16/5 ( download)

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Download or read book Measure, Integral and Probability written by Marek Capinski and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.

Author : P. E. Kopp
Publisher : Cambridge University Press
ISBN 13 : 9780521090339
Total Pages : 0 pages
Book Rating : 4.34/5 ( download)

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Download or read book Martingales and Stochastic Integrals written by P. E. Kopp and published by Cambridge University Press. This book was released on 2008-11-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the rapidly expanding theory of stochastic integration and martingales. The treatment is close to that developed by the French school of probabilists, but is more elementary than other texts. The presentation is abstract, but largely self-contained and Dr Kopp makes fewer demands on the reader's background in probability theory than is usual. He gives a fairly full discussion of the measure theory and functional analysis needed for martingale theory, and describes the role of Brownian motion and the Poisson process as paradigm examples in the construction of abstract stochastic integrals. An appendix provides the reader with a glimpse of very recent developments in non-commutative integration theory which are of considerable importance in quantum mechanics. Thus equipped, the reader will have the necessary background to understand research in stochastic analysis. As a textbook, this account will be ideally suited to beginning graduate students in probability theory, and indeed it has evolved from such courses given at Hull University. It should also be of interest to pure mathematicians looking for a careful, yet concise introduction to martingale theory, and to physicists, engineers and economists who are finding that applications to their disciplines are becoming increasingly important.

Author : P. Hall
Publisher : Academic Press
ISBN 13 : 1483263223
Total Pages : 321 pages
Book Rating : 4.29/5 ( download)

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Download or read book Martingale Limit Theory and Its Application written by P. Hall and published by Academic Press. This book was released on 2014-07-10 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.

Author : Rene L. Schilling
Publisher :
ISBN 13 : 9781108161275
Total Pages : 0 pages
Book Rating : 4.78/5 ( download)

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Download or read book Measures, Integrals and Martingales written by Rene L. Schilling and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Sheldon Axler
Publisher : Springer Nature
ISBN 13 : 3030331431
Total Pages : 430 pages
Book Rating : 4.36/5 ( download)

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Download or read book Measure, Integration & Real Analysis written by Sheldon Axler and published by Springer Nature. This book was released on 2019-11-29 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/

Author : Jean-François Le Gall
Publisher : Springer
ISBN 13 : 3319310895
Total Pages : 273 pages
Book Rating : 4.93/5 ( download)

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Download or read book Brownian Motion, Martingales, and Stochastic Calculus written by Jean-François Le Gall and published by Springer. This book was released on 2016-04-28 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô’s formula, the optional stopping theorem and Girsanov’s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.

Author : David Pollard
Publisher : Cambridge University Press
ISBN 13 : 9780521002899
Total Pages : 372 pages
Book Rating : 4.93/5 ( download)

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Download or read book A User's Guide to Measure Theoretic Probability written by David Pollard and published by Cambridge University Press. This book was released on 2002 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.